Need help with a special relativity problem

In summary, the conversation discusses a series of experiments involving three spaceships moving at the same velocity in space, with a fourth observer on Earth. By sending light pulses between the spaceships and comparing the time recorded by the fourth observer, it is determined that time runs slower at the third spaceship and faster at the first spaceship. However, there is a contradiction in the results of the second and third experiments, where time cannot be both faster and slower at the same time for the fourth observer in relation to the second spaceship. Further analysis is suggested, such as creating a space-time diagram and using Lorentz transforms to better understand the results.
  • #1
thetrice
19
0
The example given is as follows : we have 3 space ships(numbered from left to right) placed in space moving at velocity V in the same direction (they are moving to the right) , each one can send a pulse of light to the others and the others can determine time reached. so each of them is an observer , there is a fourth observer standing on earth(which is still according to his reference).

Now we want to determine who appears to have slower time or faster according to fourth observer , so the following experiments are being done :
observer 2 (the middle space ship) sends 2 light pulses to spaceship 1(first spaceship) and 2(last ship on the right) according to the first 3 observers they all appear still to each other. so they will see light reaching from 2->1 and 2->3 , at the same time X , now observer 4 sees them all 3 moving with velocity V , when the even occurred according to him, the light reached to 1 first observer before reaching the third, but since 1st observer recorded a longer time , then time runs faster to him and the third observer will record a time shorter than what should be recorded from fourth perspective so time runs slower at 3rd.

Conclusion from 1st experiment: Time runs slower at 3rd and faster at 1st.

Now repeat experiment but sending the pulse from the 1st observer to the 2nd and 3rd.
according to the first three everything is fine and running at the same speed , according to fourth observer, light will reach 2nd and third in longer time than that recorded by them meaning time is slower in 2nd and third.

Conclusion from 2nd experiment: Time runs slower at 2nd and at 3rd.

No contradictions so far Now here is the problem :

Repeating the procedure by sending pulse this time from third observer to the 1st and 2nd, again for them everything appears to run at same time , but for fourth light will reach 2nd and first in shorter time than that recorded by 1st and 2nd , so that means that time runs faster at both 1st and 2nd.

Conclusion from 3rd experiment: Time runs faster at 1st and at 2nd.

The contradiction lies between experiment 2 and 3 where time can't be faster and slower at the same time for observer 4 regarding observer 2 .

So any ideas ?

Thanks and Best Regards,
Omar Shaaban Ramzy.
 
Physics news on Phys.org
  • #2
thetrice said:
The example given is as follows : we have 3 space ships(numbered from left to right) placed in space moving at velocity V in the same direction (they are moving to the right),
relative to the fourth observer on earth?

each one can send a pulse of light to the others and the others can determine time reached. so each of them is an observer , there is a fourth observer standing on earth(which is still according to his reference).
Every observer is "still according to his reference"! I believe you are saying that everything is to calculated relative to this fourth observer.

Now we want to determine who appears to have slower time or faster according to fourth observer,
You have already said that they are all moving at speed V (relative to the fourth observer?) so should all have the same "time rate" according to that observer.

so the following experiments are being done :
observer 2 (the middle space ship) sends 2 light pulses to spaceship 1(first spaceship) and 2(last ship on the right) according to the first 3 observers they all appear still to each other. so they will see light reaching from 2->1 and 2->3 , at the same time X , now observer 4 sees them all 3 moving with velocity V , when the even occurred according to him, the light reached to 1 first observer before reaching the third, but since 1st observer recorded a longer time , then time runs faster to him and the third observer will record a time shorter than what should be recorded from fourth perspective so time runs slower at 3rd.

Conclusion from 1st experiment: Time runs slower at 3rd and faster at 1st.

Now repeat experiment but sending the pulse from the 1st observer to the 2nd and 3rd.
according to the first three everything is fine and running at the same speed , according to fourth observer, light will reach 2nd and third in longer time than that recorded by them meaning time is slower in 2nd and third.

Conclusion from 2nd experiment: Time runs slower at 2nd and at 3rd.

No contradictions so far Now here is the problem :

Repeating the procedure by sending pulse this time from third observer to the 1st and 2nd, again for them everything appears to run at same time , but for fourth light will reach 2nd and first in shorter time than that recorded by 1st and 2nd , so that means that time runs faster at both 1st and 2nd.

Conclusion from 3rd experiment: Time runs faster at 1st and at 2nd.

The contradiction lies between experiment 2 and 3 where time can't be faster and slower at the same time for observer 4 regarding observer 2 .

So any ideas ?

Thanks and Best Regards,
Omar Shaaban Ramzy.
 
  • #3
so according to the fourth observer what happens when 1st sends to the 2nd and third and when third sends to 1st and 2nd ?
 
  • #4
thetrice said:
So any ideas ?

This would be a really good time to draw a space-time diagram to see exactly what's going on. Regular poster ghwellsjr has software for drawing these, and if he's around today he'll probably chime in.

The other thing you should try is to write down the times and positions of emission and reception of each light signal using the frame in which the the spaceships are at rest, then use the Lorentz transforms to convert the coordinates of these into the frame of the fourth observer. Look carefully at these, don't forget relativity of simultaneity for all events that happen at different spatial locations, and you should be able to find the correct results:
- All observers agree that all three spaceship clocks run at the same speed.
- In the frame in which the fourth observer is at rest, the spaceship clocks are all running slow compared with the clock that is at rest in that frame.
- In the frame in which the three ships are at rest, the fourth observer's clock is running slow compared with the three spaceship clocks.

If you get different results than this... Show your work and we'll be able to help you spot where your calculation went astray.
 
Last edited:
  • #5
thetrice said:
The example given is as follows : we have 3 space ships(numbered from left to right) placed in space moving at velocity V in the same direction (they are moving to the right) , each one can send a pulse of light to the others and the others can determine time reached. so each of them is an observer , there is a fourth observer standing on earth(which is still according to his reference).

Now we want to determine who appears to have slower time or faster according to fourth observer , so the following experiments are being done :
observer 2 (the middle space ship) sends 2 light pulses to spaceship 1(first spaceship) and 2(last ship on the right) according to the first 3 observers they all appear still to each other. so they will see light reaching from 2->1 and 2->3 , at the same time X , now observer 4 sees them all 3 moving with velocity V , when the even occurred according to him, the light reached to 1 first observer before reaching the third, but since 1st observer recorded a longer time , then time runs faster to him and the third observer will record a time shorter than what should be recorded from fourth perspective so time runs slower at 3rd.

Conclusion from 1st experiment: Time runs slower at 3rd and faster at 1st.

Now repeat experiment but sending the pulse from the 1st observer to the 2nd and 3rd.
according to the first three everything is fine and running at the same speed , according to fourth observer, light will reach 2nd and third in longer time than that recorded by them meaning time is slower in 2nd and third.

Conclusion from 2nd experiment: Time runs slower at 2nd and at 3rd.

No contradictions so far Now here is the problem :

Repeating the procedure by sending pulse this time from third observer to the 1st and 2nd, again for them everything appears to run at same time , but for fourth light will reach 2nd and first in shorter time than that recorded by 1st and 2nd , so that means that time runs faster at both 1st and 2nd.

Conclusion from 3rd experiment: Time runs faster at 1st and at 2nd.

The contradiction lies between experiment 2 and 3 where time can't be faster and slower at the same time for observer 4 regarding observer 2 .

So any ideas ?

Thanks and Best Regards,
Omar Shaaban Ramzy.
I think your problem is that you are relying on what the Earth observer actually sees and is using his own clock to establish the times that the remote events occur without taking into account the time it takes for the images to transit from those remote events to the Earth observer.

As Nugatory said, I will draw some spacetime diagrams, but I won't have them ready for at least a day. In the meantime, it would be good for you to think about the light transit times and how that might resolve the discrepancies in your analysis.
 
  • #6
thetrice said:
The example given is as follows : we have 3 space ships(numbered from left to right) placed in space moving at velocity V in the same direction (they are moving to the right) , each one can send a pulse of light to the others and the others can determine time reached. so each of them is an observer , there is a fourth observer standing on earth(which is still according to his reference).
I'm going to take a stab at trying to interpret what your reasoning is and then you can tell me if I'm understanding you correctly.

thetrice said:
Now we want to determine who appears to have slower time or faster according to fourth observer , so the following experiments are being done :
observer 2 (the middle space ship) sends 2 light pulses to spaceship 1(first spaceship) and [STRIKE]2[/STRIKE] 3 (last ship on the right) according to the first 3 observers they all appear still to each other. so they will see light reaching from 2->1 and 2->3 , at the same time X ,
Here's a spacetime diagram for the rest frame of the three spaceships which I have spaced 2000 feet apart in their rest frame. Space ship 1 is depicted in red, 2 is in black and 3 is in green. The middle one has sent a pulse of light to the two outside space ships. The light pulses arrive in 2 microseconds since the outside space ships are 2000 feet away from the middle one and the speed of light is 1000 feet per microsecond. The Earth observer 4 is shown in blue moving away at -0.6c:

attachment.php?attachmentid=71311&stc=1&d=1405314916.png

thetrice said:
now observer 4 sees them all 3 moving with velocity V , when the event occurred according to him, the light reached to 1 first observer before reaching the third, but since 1st observer recorded a longer time , then time runs faster to him and the third observer will record a time shorter than what should be recorded from fourth perspective so time runs slower at 3rd.

Conclusion from 1st experiment: Time runs slower at 3rd and faster at 1st.
Here is the first spacetime diagram transformed to a speed of -0.6c so that the blue Earth observer 4 is now stationary and the space ships are traveling to the right at 0.6c:

attachment.php?attachmentid=71312&stc=1&d=1405314981.png

I think what you are noticing is that what took 2 microseconds in the rest frame of the space ships takes 1 microsecond for spaceship 1 (red) and 4 microseconds for spaceship 3 (green) and this is why you came to your conclusion, correct?

thetrice said:
Now repeat experiment but sending the pulse from the 1st observer to the 2nd and 3rd.
according to the first three everything is fine and running at the same speed ,
Here's the second experiment's spacetime diagram for the rest frame of the space ships:

attachment.php?attachmentid=71313&stc=1&d=1405315553.png

It takes 2 microseconds for the light pulse to get from 1 (red) to 2 (black) and 4 microseconds to get from 1 (red) to 3 (green).

thetrice said:
according to fourth observer, light will reach 2nd and third in longer time than that recorded by them meaning time is slower in 2nd and third.

Conclusion from 2nd experiment: Time runs slower at 2nd and at 3rd.
Here's the second experiment's spacetime diagram for the rest frame of the blue Earth observer 4:

attachment.php?attachmentid=71314&stc=1&d=1405315553.png

For the Earth observer, the times are now 4 microseconds to get to spaceship 2 (black) and 8 microseconds to get to spaceship 3 (green), double what it took in the space ship's frame, therefore your conclusion that time is slower in this case, correct?

thetrice said:
No contradictions so far Now here is the problem :

Repeating the procedure by sending pulse this time from third observer to the 1st and 2nd, again for them everything appears to run at same time ,

Here's the third experiment's spacetime diagram for the rest frame of the space ships:

attachment.php?attachmentid=71315&stc=1&d=1405316515.png

It takes 2 microseconds for the light pulse to get from 3 (green) to 2 (black) and 4 microseconds to get from 3 (green) to 1 (red).

thetrice said:
but for fourth light will reach 2nd and first in shorter time than that recorded by 1st and 2nd , so that means that time runs faster at both 1st and 2nd.

Conclusion from 3rd experiment: Time runs faster at 1st and at 2nd.

Finally, we have the third experiment's rest frame for the Earth observer:

attachment.php?attachmentid=71316&stc=1&d=1405317790.png

For the Earth observer, the times are now 1 microsecond to get to spaceship 2 (black) and 2 microseconds to get to spaceship 1 (red), half what it took in the space ship's frame, therefore your conclusion that time is faster in this case, correct?

thetrice said:
The contradiction lies between experiment 2 and 3 where time can't be faster and slower at the same time for observer 4 regarding observer 2 .

So any ideas ?

Thanks and Best Regards,
Omar Shaaban Ramzy.
Did I adequately describe your concern?
 

Attachments

  • 3Spaceships1.PNG
    3Spaceships1.PNG
    4.5 KB · Views: 482
  • 3Spaceships2.PNG
    3Spaceships2.PNG
    4.5 KB · Views: 493
  • 3Spaceships3.PNG
    3Spaceships3.PNG
    4.7 KB · Views: 450
  • 3Spaceships4.PNG
    3Spaceships4.PNG
    4.6 KB · Views: 467
  • 3Spaceships5.PNG
    3Spaceships5.PNG
    4.6 KB · Views: 488
  • 3Spaceships6.PNG
    3Spaceships6.PNG
    4.3 KB · Views: 473
  • Like
Likes 1 person
  • #7
Thanks ghwellsjr, a far well written reply , yes you adequately describe my concern.

Now this actually describes my question perfectly,My question is would the Earth observer see ship number 2(black) to be faster or slower ? or that only depends on from where i send the pulse ?

as sometimes it appears to me to be slower and sometimes faster in time,but ship 1(red) and 3(green) always appear to be running with constant different time rate for observer 4(blue), while observer 2(black) has variable time rate to observer 4(blue).

Again much thanks for your effort.
 
  • #8
thetrice said:
Thanks ghwellsjr, a far well written reply , yes you adequately describe my concern.
Good, I was hoping so.

thetrice said:
Now this actually describes my question perfectly,My question is would the Earth observer see ship number 2(black) to be faster or slower ? or that only depends on from where i send the pulse ?
It's not from where the pulse is sent but rather the direction in which it is sent. The light pulses that are directed away from the Earth observer take longer to make the trip according to the Earth observer's rest frame than they do according to the ships' rest frame. And the light pulses that are directed toward the Earth observer take less time to make the trip according to the Earth observer's rest frame than they do according to the ships' rest frame.

thetrice said:
as sometimes it appears to me to be slower and sometimes faster in time,but ship 1(red) and 3(green) always appear to be running with constant different time rate for observer 4(blue), while observer 2(black) has variable time rate to observer 4(blue).
Since you are always comparing the light pulse transit times from one ship to another, you can't attribute the differences to just one ship. It only appears that the black ship is different because it can receive light pulses from either direction, since it is in the middle. The other two ships can only receive light pulses from one direction.

thetrice said:
Again much thanks for your effort.
You're welcome and I hope these added comments clarify the issue for you.
 

1. What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes how the laws of physics work in reference frames that are moving at a constant velocity relative to each other. It states that the laws of physics are the same for all observers in these frames and that the speed of light is constant regardless of the observer's frame of reference.

2. What is a special relativity problem?

A special relativity problem is a question or scenario that involves applying the principles of special relativity to solve for unknown quantities or understand the behavior of objects in different reference frames.

3. How do I approach solving a special relativity problem?

To solve a special relativity problem, you should first identify the reference frames involved and determine their relative velocities. Then, use the equations of special relativity, such as the Lorentz transformation, to calculate the quantities you are looking for.

4. What are some common mistakes when solving special relativity problems?

Some common mistakes when solving special relativity problems include forgetting to account for the time dilation and length contraction effects, using incorrect units for velocity or time, and not considering the direction of motion in calculations.

5. How is special relativity important in real-world applications?

Special relativity has many practical applications, such as in the development of GPS technology, particle accelerators, and nuclear energy. It also helps us understand the behavior of objects traveling at high speeds, such as spacecraft, and plays a crucial role in modern physics theories, including the theory of general relativity.

Similar threads

  • Special and General Relativity
2
Replies
57
Views
4K
Replies
32
Views
852
  • Special and General Relativity
Replies
14
Views
582
  • Special and General Relativity
Replies
20
Views
747
  • Special and General Relativity
Replies
20
Views
1K
  • Special and General Relativity
Replies
16
Views
615
  • Special and General Relativity
Replies
21
Views
522
  • Special and General Relativity
2
Replies
62
Views
3K
  • Special and General Relativity
Replies
17
Views
440
  • Special and General Relativity
2
Replies
37
Views
2K
Back
Top